函数的Fuzzy极限

摘要：

本文的目的是介绍和研究函数的模糊极限。两种方法来模糊极限的函数被认为是。一个是基于序列的模糊极限的概念，而另一个是推广了传统的ε-δ定义。证明了这些构造是等价的。给出了函数模糊极限的不同性质，并由模糊极限的性质导出了常规极限的性质。在这项工作的第二部分，模糊极限的概念的一个功能扩展到提供手段来定义非平凡的连续性的功能离散集。此外，还引入并研究了函数的模糊极限。

英文摘要：

The goal of this work is to introduce and study fuzzy limits of functions. Two approaches to fuzzy limits of a function are considered. One is based on the concept of a fuzzy limit of a sequence, while another generalizes the conventional epsilon-delta definition. It is demonstrated that these constructions are equivalent. Different properties of fuzzy limits of functions are found. Properties of conventional limits are easily deduced from properties of fuzzy limits. In the second part of this work, the concept of fuzzy limits of a function is extended to provide means to define nontrivial continuity of functions on discrete sets. In addition, fuzzy limits of functions are introduced and studied.

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